This can be confusing for a lot of people, but if plan on conducting business in a state other than that of your incorporation (or LLC formation), in this case Illinois, you are more than likely going to have to register your business in the other state, California. It is referred to as foreign qualification.
Yes! if you’re physically running camps in California, your Illinois entity will usually need to register as a “foreign entity” in California. That means filing with the CA Secretary of State and paying annual franchise taxes/fees.
You don’t necessarily need a new company, but you do need to be compliant in every state where you’re actively doing business. Since each state’s rules differ a bit, it’s smart to double-check with a CPA or attorney so you don’t miss ongoing filing or tax obligations.